Analysis Seminar

Sanaz Pooya, Stockholm University

"On the Baum-Connes assembly map for certain semi-direct products"

The Baum-Connes conjecture for a group $G$ predicts that the assembly map 
$
\mu^G_i\colon \mathrm{K_i^G}(\underline{\mathrm E}G)\rightarrow \mathrm {K_i}(C_{\mathrm r}^*G) 
$
is an isomorphism for $ i=0, 1$. A breakthrough result of Higson and Kasparov shows that a-T-menable groups satisfy the conjecture, hence the group $G = F\wr \mathbb F_n$, where $F$ is finite and $\mathbb F_n$ is a free group. This result however does not describe the K-groups. In this talk, we shed light on the assembly map for this group and describe it explicitly. In doing so we reprove the conjecture for this group.

MC 5417